CALCULUS. Check my answers, please! :)

The domain of f(x)=(1)/(sqrt(x^2-6x-7)) is

(1, 7)
[-1, 7]
x > -1 or x < 7
***{x < -1}U{x > 7}
(-∞, -1]U[7, ∞)

2. In which of the following is y a function of x?
I. y^2=9-x^2
II. |y|=x
III. y=(sqrt(x^2))^3

I only
II only
III only
***I and III only
I, II and III

3. You would probably use calculus to determine the area for which of the following shapes?

***(infinity symbol)
(rectangle)
(triangle)
(arrow)
(plus sign)

4. If g(x)=3x−1 and f(x)=(sqrt(9-x^2)) , then which of the following will have a domain of: [−3, 1/3) ∪ (1/3, 3]?

(g + f)(x)
(f/g)(x)
(g − f)(x)
***g(f(x))
f(g(x))

5. Which of the following is always true of odd functions?

I. f(-x)=-f(x)
II.f(|x|) is even
III. |f(x)| is even

All of these are true.
None of these are true.
I only.
II only.
***I and III only.

6. If f(x)= 3/(x-3), then f^-1(x)=
(x-3)/3
(x+3)/3
***3/(x+3)
3/(x-3)
No inverse exists.

7. The function f(x) = −|x − b| intersects g(x) = 2(x − 4)^2 at exactly one point. The value of b is:

-5
***-4
5
4
Any real number

8. If a right circular cone must have a volume of 12 cubic meters, then a function that gives the possible radii as a function of the height is:

r=12/pi*h
r=+-(sqrt(36/pi*h))
***r=(sqrt(36/pi*h))
h=(sqrt(36/pi*r^2))
r=36/(pi*h)

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  1. #1 ok

    #2 III only
    for y to be a function of x, each x must map to only one y.

    #3 ok

    #4 (f/g)(x)
    f has domain [-3,3]
    g has domain x≠1/3

    #5 all of the above
    f(|-x|) = f(|x|)

    #6 Hmmm. I get 3(x+1)/x = 3/x + 3
    That's your choice without the parentheses

    #7 +4

    #8 ok

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  2. Thank you!! Unfortunately I couldn't wait for your response, but I went over my answers before checking to see if they were right, and I got them all right! Thank you so much for your help! It means the world to me, and will count on you if I need help on more topics in Calculus. :)

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  3. Hey Samantha, were his answers right or were yours?

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  4. his answers are right

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